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Joined 2026-09-21 Message
Incoming links: Imperative programming
Past exam of the mathematics course of the University of Cambridge 2007 ia Paper 5 6 a Solution Created 2026-09-24 Updated 2026-10-14
An ML reference type Both dereferences now give one. A reference's stored type remains fixed; the value restriction prevents allocating one unrestricted polymorphic cell and then using incompatible instantiations.
'a ref describes a mutable cell holding a value of type 'a. The operations are ref : 'a -> 'a ref for allocation, ! : 'a ref -> 'a for dereferencing and := : 'a ref * 'a -> unit for assignment. An immutable variable binding can name a mutable cell; assigning to the cell does not change what the binding denotes. Two names may alias the same cell, so an update through either is visible through the other.val counter = ref 0;
val alias = counter;
counter := !counter + 1;Imperative programming uses sequencing References provide mutable state; sequencing, conditionals and loops control its updates.
(e1; e2; ...; en) to perform effects left to right, with the final expression supplying the result. Conditional expressions choose one branch. while condition do body repeatedly checks a Boolean condition and performs a unit-valued body, returning () on termination. Standard ML has no required primitive for loop, but recursion or a reference with while supplies one. For example:fun sumTo n =
let val i = ref 1
val total = ref 0
in
while !i <= n do
(total := !total + !i; i := !i + 1);
!total
end;